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Extended phase space thermodynamics for charged and rotating black holes and Born-Infeld vacuum polarization

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Abstract

We investigate the critical behaviour of charged and rotating AdS black holes in d spacetime dimensions, including effects from non-linear electrodynamics via the Born-Infeld action, in an extended phase space in which the cosmological constant is interpreted as thermodynamic pressure. For Reissner-Nördstrom black holes we find that the analogy with the Van der Walls liquid-gas system holds in any dimension greater than three, and that the critical exponents coincide with those of the Van der Waals system. We find that neutral slowly rotating black holes in four space-time dimensions also have the same qualitative behaviour. However charged and rotating black holes in three spacetime dimensions do not exhibit critical phenomena. For Born-Infeld black holes we define a new thermodynamic quantity B conjugate to the Born-Infeld parameter b that we call Born-Infeld vacuum polarization. We demonstrate that this quantity is required for consistency of both the first law of thermodynamics and the corresponding Smarr relation.

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Authors and Affiliations

  1. Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario, N2L 3G1, Canada

    Sharmila Gunasekaran & Robert B. Mann

  2. Perimeter Institute, 31 Caroline St. N, Waterloo, Ontario, N2L 2Y5, Canada

    David Kubizňák

Authors
  1. Sharmila Gunasekaran
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  2. David Kubizňák
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  3. Robert B. Mann
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Correspondence to David Kubizňák.

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ArXiv ePrint: 1208.6251

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Gunasekaran, S., Kubizňák, D. & Mann, R.B. Extended phase space thermodynamics for charged and rotating black holes and Born-Infeld vacuum polarization. J. High Energ. Phys. 2012, 110 (2012). https://doi.org/10.1007/JHEP11(2012)110

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